DISTANCE COMPUTING FORM — ANDOYER-LAMBERT 



TYPE APPROXIMATION WITH SECOND ORDER TERMS 



(No conversion to parametric latitudes) 



Clarke Spheroid 1866, a = 6,378,206.4 meters 



f/2 = 0.00169503765, f/4 = 0.000847518825, fVl28 = 0.0897860195 x 10"' 



O 1 11 O 1 11 



slch, ' 9Sf ^r^^d'^ 2. west of 1. AA^aJa, r Ji^ ^/' ^ ^S 



COS ^, -^•»<5'" ^^^^^ sin 0, ^ f^ f ^/■<^'^^ ^\n AA ^> ^^^'^ ^.T;^^' 



tan rh, --^' ^/f /^r^J-S- ,„3 ^^ .Sy^ ^-^-^^^ cos AA ^. y/-9 .^J-sT^^ 



tan 0; «^ - y^y ^ ^Vr V cos d = sin (^^ sin 02 + cos 0i cos 02 cos A A •• Z 7^ ^Si^^a 



M = cos 0^ tan 0^ - sin 0^ cos AA ^- '^^^'^ yS^-^ y<^ cot u = M/sin AA '^' /S f J?^ 9 f t^:. 



N = cos 02 tan 0,- sin 0^ cos AA " ' ^^^^^ g^<;^ ^ T^^'^ ^^ cot v = N/sin AA — - C^<^cy^ ^'S^V9~ S^O ^ 

 sin d = cos 0,sinAA/sin v = cos 02sinAA/sin n 7^>«£-^5-g' -^ 9>'6',J u J^.^ ^g' -^ ^^ ^^ ,^ 



CSC d -^/^' S'fi^ gJ^'/S cot d -r^^9. f.<r ^<i'^<^ V ^^> ^^- x?^. j'» ^.2_ 



1 + cos d ?*•/- 9ff <^y^s''f' 1-cos d 7^,c^^y^c<s V ^ sin u ■ ^. 9rc?s'yyiP<^ 



(sin ,^, + sinrAJ V-i'-^^-^^'^/:!^/-g^ (sin0,-sin^j V> -//.^-^^X/^ ' "^sin v - /- <:^-^^' ^^^^^ 

 Ki = (sin0i + sin02)V(l + cos Hi //' ■7(iV fySJ'? l^^^f^jn rA,-s.in 0^WO-rns dl ^T ^ <i"^ / // f/ -^ 



V = K , + ic ^ y-/. 7^<^^ v^^^ Y=K^-K, y-A ^(iSJ^^^y^ xy -?^x/. //^ 9^^ 9^^ 



A-64d +16d'cotd :^ ^^ ^^ ^ ¥ -^^^^S^ n = 4«sin d +8d/ esc d 7"^> JV^ ^ <^ 9 S^ 



c= -(30d, +8d/ rot d +F/91 -J- y// sf30'? AX -y- 7, /^<^ /^y<>r 



RY — £ ^i/'^ //^ ^^ rx^ -/g^. 6ii/<^ V/v^ nxY 7^^^ ^^^J' S'/^'^f 



EY' /-/. •S^Kfi'f^ ^ i^ S=AX + RY+CX^ + nXY + EY^ 7-^. ^^^^^-T .T^^^^ 



;?d^^-ff/dUXd^-qY.indi T^^^^g'^^Xj-^^/'^^ Mj^^^ffVi^Riy 7^ a'^cp^:?^^ V/ f" 



s(sdf) = a(d^ + /;df) -3*-^<^ f^^, 9^9 s(5dp) = a{dr + 5df + sdp)^£i3y/^;rr^_fy ^ 



sin 2u -^'^^9/ >? <>^? y^/ sin 2v ^^e?^ ^^99^ 



U = (f/2) cos^0, sin 2n y-^ ^'^/ 9 / /O ^'^ V =(f/2) cos^cA. sin 2v ^.J>,/f/ Y /<i:?j; ^ " 



VT — ^ vra y y^^r^ - y TIT v->r; yr^ y^^ --^ 



^n ^ VT-Ti — ■:r. y^/J^i^ y /^ -<^ ;;v ^ -TIT + V -^T^ -/ f^ ^ xf /^ - ^^ 



+ Su j!:r /A j'Z/ + Sv_= //. J'//^ 



a 1-2 



+180 o . 1, +180 o I 11 



- a. 



= 180°- u + Su a, = a„„ = 180° + v + 5v 



Line No. 3, See Tables 1 and 2. True distance 



128 



^j>/, U6 ' 796 



